基于改进型直流潮流算法的主动配电网分布式电源规划模型及其线性化方法
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摘要
以分布式电源(distributed generation,DG)运营商净收益最大为优化目标,建立多场景多时段耦合的主动配电网分布式电源规划模型。首先针对传统分布式电源规划求解方法的不足,提出一种计及电压和无功功率的改进型直流潮流模型,实现支路潮流方程中电压幅值与相角的解耦,并基于此建立了考虑储能系统和多种主动管理(activemanagement,AM)措施协调优化的分布式电源规划模型。其次,在保证模型精度和系统运行物理意义的前提下,引入网损因子法、圆形约束线性化法、McCormick凸包络线法、辅助变量等方法,将原始模型转换为混合整数线性优化模型。最后,提出了一种基于热启动(warm start)的迭代求解流程以保证模型精度。以江苏省某市经济开发区的15节点系统为测试算例,调用GAMS-MOSEK求解器对规划模型进行求解,验证了模型及算法的有效性。
Aiming for maximizing net profit of system operator, a distributed generation planning model of active distribution network is established in multiple scenes. In view of the shortcomings of traditional methods, an improved DC power flow model considering voltage and reactive power is proposed to realize decoupling of voltage amplitude and phase angle in branch flow equations and, based on this model, a planning model is built, considering energy storage system and some active management measures. Then, on premise of ensuring accuracy and physical meaning of the system, linearization of the model is realized by means of network loss factor method, circular constraint linearization, McCormick convex envelope method and auxiliary variable method, transforming the original model into a mixed integer linear optimization model. Finally, an iterative solution process based on warm start is proposed to ensure accuracy of the model. Taking a 15-node system of an economic development zone in Jiangsu Province as a study case, the GAMS-MOSEK solver is called to solve the problem, verifying validity of the model and algorithm.
Aiming for maximizing net profit of system operator, a distributed generation planning model of active distribution network is established in multiple scenes. In view of the shortcomings of traditional methods, an improved DC power flow model considering voltage and reactive power is proposed to realize decoupling of voltage amplitude and phase angle in branch flow equations and, based on this model, a planning model is built, considering energy storage system and some active management measures. Then, on premise of ensuring accuracy and physical meaning of the system, linearization of the model is realized by means of network loss factor method, circular constraint linearization, McCormick convex envelope method and auxiliary variable method, transforming the original model into a mixed integer linear optimization model. Finally, an iterative solution process based on warm start is proposed to ensure accuracy of the model. Taking a 15-node system of an economic development zone in Jiangsu Province as a study case, the GAMS-MOSEK solver is called to solve the problem, verifying validity of the model and algorithm.
引文
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[20]Yang Z,Zhong H,Xia Q,et al.Optimal power flow based on successive linear approximation of power flow equations[J].IETGeneration Transmission&Distribution,2016,10(14):3654-3662.
[21]Yang Z,Bose A,Zhong H,et al.Optimal reactive power dispatch with accurately modeled discrete control devices:a successive linear approximation approach[J].IEEE Transactions on Power Systems,2016,PP(99):1-1.
[22]丁明,史盛亮,潘浩,等.含电动汽车充电负荷的交直流混合微电网规划[J].电力系统自动化,2018,42(1):32-36.Ding Ming,Shi Shengliang,Pan Hao,et al.Planning of AC/DChybrid microgrid with integration of electric vehicles charging load[J].Automation of Electric Power Systems,2018,42(1):32-36(in Chinese).
[23]Yang Z,Zhong H,Xia Q,et al.A novel network model for optimal power flow with reactive power and network losses[J].Electric Power Systems Research,2017(144):63-71.
[24]刘一兵,吴文传,张伯明,等.基于混合整数二阶锥规划的三相有源配电网无功优化_刘一兵[J].电力系统自动化,2014,38(15):58-64.Liu Yibing,Wu Wenchuan,Zhang Boming,et al.Reactive power optimization for three-phase distribution networks with distributed generators based mixed integer second-order cone programming[J].Automation of Electric Power Systems,2014,38(15):58-64(in Chinese).
[25]Chen X,Wu W,Zhang B,et al.Data-driven DG capacity assessment method for active distribution networks[J].IEEE Transactions on Power Systems,2017,PP(99):1-1.
[26]Ding T,Bo R,Li F,et al.A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses[J].IEEE Transactions on Power Systems,2015,30(6):2841-2855.
[2]吕涛,唐巍,丛鹏伟,等.分布式电源与配电网架多目标协调规划[J].电力系统自动化,2013,37(21):139-145.LüTao,Tang Wei,Cong Pengfei,et al.Multi-objective coordinated planning of distribution network incorporating distributed generators[J].Automation of Electric Power Systems,2013,37(21):139-145(in Chinese).
[3]郭金明,李欣然,邓威,等.基于2层规划的间歇性分布式电源及无功补偿综合优化配置[J].中国电机工程学报,2013,33(28):25-33.Guo Jinming,Li Xinran,Deng Wei,et al.Comprehensive optimal allocation of intermittent distributed generation and reactive power compensation based on bilevel planning[J].Proceedings of the CSEE,2013,33(28):25-33(in Chinese).
[4]Zheng Y,Dong Z Y,Luo F J,et al.Optimal allocation of energy storage system for risk mitigation of DISCOs with high renewable penetrations[J].IEEE Transactions on Power Systems,2013,29(1):212-220.
[5]曾鸣,舒彤,史慧,等.兼顾分布式发电商利益的有源配电网规划[J].电网技术,2015,39(5):1379-1383.Zeng Ming,Shu Tong,Shi Hui,et al.An active distribution network planning taking interest of distributed genco into account[J].Power System Technology,2015,39(5):1379-1383(in Chinese).
[6]张沈习,李珂,程浩忠,等.考虑相关性的间歇性分布式电源选址定容规划[J].电力系统自动化,2015,39(8):53-58.Zhang Shenxi,Li Ke,Cheng Haozhong,et al.Optimal siting and sizing of intermittent distributed generator considering correlations[J].Automation of Electric Power Systems,2015,39(8):53-58(in Chinese).
[7]董雷,田爱忠,于汀,等.基于混合整数半定规划的含分布式电源配电网无功优化[J].电力系统自动化,2015,39(21):66-72.Dong Lei,Tian Aizhong,Yu Ting,et al.Reactive power optimization for distribution network with distributed generators based on mixed integer semidefinite programming[J].Automation of Electric Power Systems,2015,39(21):66-72(in Chinese).
[8]Lavaei J,Low S H.Zero duality gap in optimal power flow problem[J].IEEE Transactions on Power Systems,2012,27(1):92-107.
[9]Farivar M,Low S H.Branch flow model:relaxations and convexification-part II[J].IEEE Transactions on Power Systems,2012,28(3):2565-2572.
[10]Li Q,Vittal V.Convex hull of the quadratic branch AC power flow equations and its application in radial distribution networks[J].IEEETransactions on Power Systems,2017,PP(99):1-1.
[11]Alves M J,Dempe S,Júdice J J.Computing the pareto frontier of a bi-objective bi-level linear problem using a multiobjective mixedinteger programming algorithm[J].Optimization,2012,61(3):335-358.
[12]Nick M,Cherkaoui R,Leboudec J Y,et al.An exact convex formulation of the optimal power flow in radial distribution networks including transverse components[J].IEEE Transactions on Automatic Control,2016,PP(99):1-1.
[13]Ding T,Li C,Li F,et al.A bi-objective DC-optimal power flow model using linear relaxation-based second order cone programming and its pareto frontier[J].International Journal of Electrical Power&Energy Systems,2017(88):13-20.
[14]Christakou K,Tomozei D C,Boudec J Y L,et al.AC OPF in radial distribution networks-part I:on the limits of the branch flow convexification and the alternating direction method of multipliers[J].Electric Power Systems Research,2017(143):438-450.
[15]高红均,刘俊勇,沈晓东,等.主动配电网最优潮流研究及其应用实例[J].中国电机工程学报,2017,37(6):1634-1644.Gao Hongjun,Liu Junyong,Shen Xiaodong,et al.Optimal power flow research in active distribution network and its application examples[J].Proceedings of the CSEE,2017,37(6):1634-1644(in Chinese).
[16]Christakou K,Tomozei D C,Boudec J Y L,et al.AC OPF in radial distribution networks-part II:an augmented lagrangian-based OPFalgorithm,distributable via primal decomposition[J].Electric Power Systems Research,2017(150):24-35.
[17]Yang Z,Zhong H,Bose A,et al.A linearized OPF model with reactive power and voltage magnitude:a pathway to improve the MW-only DCOPF[J].IEEE Transactions on Power Systems,2017,PP(99):1-1.
[18]Garces A.A linear three-phase load flow for power distribution systems[J].IEEE Transactions on Power Systems,2015,31(1):827-828.
[19]Ahmadi H,Mart?′J R,Meier A V.A linear power flow formulation for three-phase distribution systems[J].IEEE Transactions on Power Systems,2016,31(6):5012-5021.
[20]Yang Z,Zhong H,Xia Q,et al.Optimal power flow based on successive linear approximation of power flow equations[J].IETGeneration Transmission&Distribution,2016,10(14):3654-3662.
[21]Yang Z,Bose A,Zhong H,et al.Optimal reactive power dispatch with accurately modeled discrete control devices:a successive linear approximation approach[J].IEEE Transactions on Power Systems,2016,PP(99):1-1.
[22]丁明,史盛亮,潘浩,等.含电动汽车充电负荷的交直流混合微电网规划[J].电力系统自动化,2018,42(1):32-36.Ding Ming,Shi Shengliang,Pan Hao,et al.Planning of AC/DChybrid microgrid with integration of electric vehicles charging load[J].Automation of Electric Power Systems,2018,42(1):32-36(in Chinese).
[23]Yang Z,Zhong H,Xia Q,et al.A novel network model for optimal power flow with reactive power and network losses[J].Electric Power Systems Research,2017(144):63-71.
[24]刘一兵,吴文传,张伯明,等.基于混合整数二阶锥规划的三相有源配电网无功优化_刘一兵[J].电力系统自动化,2014,38(15):58-64.Liu Yibing,Wu Wenchuan,Zhang Boming,et al.Reactive power optimization for three-phase distribution networks with distributed generators based mixed integer second-order cone programming[J].Automation of Electric Power Systems,2014,38(15):58-64(in Chinese).
[25]Chen X,Wu W,Zhang B,et al.Data-driven DG capacity assessment method for active distribution networks[J].IEEE Transactions on Power Systems,2017,PP(99):1-1.
[26]Ding T,Bo R,Li F,et al.A bi-level branch and bound method for economic dispatch with disjoint prohibited zones considering network losses[J].IEEE Transactions on Power Systems,2015,30(6):2841-2855.